Quantitative Aptitude

Time, Speed and Distance

2,165 Questions
All Core formulas and unit conversion 441 Boats and streams effective speed 396 Relative speed, meetings, and overtaking 375 Average speed 362 Early and late arrival 321 Proportional relationships 202 Stoppage time per hour 35 Train and stationary or moving object crossing 17 Races and dead heats 16

Time, Speed and Distance Questions

Multiple choice

The difference between the times taken by two buses to travel a distance of 350 km is 2 hours 20 minutes. If the difference between their speeds is 5 kmph, find the slower speed.

  1. 35 kmph

  2. 30 kmph

  3. 25 kmph

  4. 20 kmph
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let speeds be v and v+5. Time difference: 350/v - 350/(v+5) = 7/3 hours. 350(v+5 - v) / (v(v+5)) = 7/3. 350 * 5 / (v^2 + 5v) = 7/3. 1750 * 3 / 7 = v^2 + 5v. 750 = v^2 + 5v. v^2 + 5v - 750 = 0. (v+30)(v-25) = 0. Slower speed v = 25.

Multiple choice

Three cars started simultaneously from Ajmer to Benaras along the same highway. The second car travelled with a speed that was 10 km/h higher than the first car's speed and arrived at Benaras 1 hour earlier than the first car. The third car arrived at Benaras 33.33 minutes earlier than the first car, travelling half the time at the speed of the first car and the other half at the speed of the second car. Find the total distance covered by these three cars during their journeybetween Ajmer and Benaras.

  1. 360 km

  2. 600 km

  3. 540 km

  4. 840 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance be D and speed of first car be v. Second car speed = v+10. Time difference = 1 hour. D/v - D/(v+10) = 1. Third car speed = (v + v+10)/2 = v+5. Time difference = 33.33 min = 1/3 hour. D/v - D/(v+5) = 1/3. Solving these equations yields D = 600 km.

Multiple choice

A person travels from his house to office using cycle in 2 hrs 30 minutes and from office to industry using company car at a speed 75 km/hr. The ratio of distances is 2: 9. The average speed is 50 km/hr. Find the speed of the cycle.

  1. 37.5 m/sec

  2. 20 km/hr

  3. 37.5 km/hr

  4. 20 m/sec

  5. 15 km/hr
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let distance to office be 2x and to industry be 9x. Total distance = 11x. Total time = 2.5 + (9x/75). Average speed = Total distance / Total time = 11x / (2.5 + 9x/75) = 50. Solving for x gives x = 25. Time for cycle = 2.5 hours, distance = 2*25 = 50 km. Speed = 50/2.5 = 20 km/hr.

Multiple choice

[CAT 1990] A car after travelling 18 km from a point A developed some problem in the engine and speed became (4/5)th of its original speed. As a result, the car reached point B 45 minutes late. If the engine had developed the same problem after travelling 30 km from A, then it would have reached B only 36 minutes late. The original speed of the car (in km per hour) and the distance between the points A and B (in km) is

  1. 25, 130

  2. 30, 150

  3. 20, 90

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

[CAT 1994] A and B walk from X to Y, a distance of 27 km at 5 kmph and 7 kmph respectively. B reaches Y and immediately turns back meeting A at Z. What is the distance from X to Z?

  1. 25 km

  2. 22.5 km

  3. 24 km

  4. 20 km
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time for B to reach Y = 27 / 7 hours. In that time, A travels 5 * (27/7) = 135/7 km. B turns back and meets A at Z. Let t be the time after B reaches Y. (5 + 7) * t = distance B traveled back = 27 - 135/7 = 54/7. t = 54/84 = 9/14 hours. Distance from X to Z = A's total distance = 5 * (27/7 + 9/14) = 5 * (54/14 + 9/14) = 5 * (63/14) = 5 * 4.5 = 22.5 km.

Multiple choice

[CAT 2008] Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to

  1. 6: 15 am

  2. 6: 30 am

  3. 6 :45 am

  4. 7: 00 am
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The train travels 500 km at 50 km/h, taking 10 hours. It arrives at 6:00 pm. Rahim needs to reach C by 5:45 pm. Using the geometry of the positions and the speed of 70 km/h, calculating the distance AC and the travel time confirms 6:30 am is the latest departure time.

Multiple choice

The question is followed by two statements, I and II. Mark the answer as per the given conditions. [CAT 1990] How long did Mr. X take to cover 5000 km journey with 10 stopovers? I. The ith stopover lasted i2 minutes. II. The average speed between any two stopovers was 66 kmph.

  1. statement I alone is required to answer the question, but not statement II.

  2. statement II alone is required to answer the question, but not statement I.

  3. both statements I and II together are needed to answer the question.

  4. cannot be answered even with the help of both the statements.
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

A and B are two stations 390 km apart. A train starts from A at 10 am and travels towards B at 65 kmph. Another train starts from B at 11 am and travels towards A at 35 kmph. At what time do they meet?

  1. 3:15 pm

  2. 2:15 pm

  3. 4:15 pm

  4. 12:15 pm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Train A starts at 10 am at 65 kmph. By 11 am, it has traveled 65 km. Remaining distance = 390 - 65 = 325 km. Relative speed = 65 + 35 = 100 kmph. Time to meet = 325 / 100 = 3.25 hours = 3 hours 15 minutes. 11 am + 3 hours 15 minutes = 2:15 pm.